The nested mesh approach has already been the subject of many studies. It is presented for example in [7] (for the sake of readability, the various documents cited are brought together in appendix 3, at the end of the present description) in the case of video image encoding.
A mesh is classically defined by a set of vertices and oriented faces (FIG. 1) defining a topology. Such meshes are used for example in computer graphics, for the modeling of objects in three dimensions with limited geometrical complexity.
The approximation of a mesh M consists in finding a mesh M′ whose geometrical complexity is lower than that of the mesh M, and that approaches the geometry of M as closely as possible.
Advantageously, the mesh M′ consists of a succession of nested meshes, each corresponding to a level of detail, or hierarchical level, so as to enable a gradual reconstruction of the images and a simplified encoding.
At each hierarchical level, the nodal values of the mesh are optimized to minimize the squared error of reconstruction. These nodal values are then quantified and encoded. A method of this kind gives efficient compression rates and limits visual deterioration. This deterioration corresponds here rather to the smoothing effects, which are less disagreeable to the human eye. This is related to the good properties of continuity of the reconstructed surfaces obtained by the method of approximation by meshes.
Furthermore, this scheme proves to be well suited to video applications. Indeed, triangular meshes prove to be more flexible and efficient for motion estimation.
However, the inventors have observed that this compression technique suffers from a sub-optimality defect. Indeed, the bases used for each level show redundancies.
Furthermore, the nested mesh technique enables the gradual reconstruction of the images, first of all at a coarse level, and then at a gradually refined level (with a scalable transmission of the images). According to the -classic technique, this approach however is not optimized: indeed, the quality obtained at each level (except for the last level) is not optimal.
There are also known image compression techniques based on the exploitation of inter-subband correlations obtained from a filtering operation implementing wavelets. These techniques permit high-performance compression rates [4] [5].
However, for applications for which there is only a very low bit rate available, the methods are seen to give considerable visual deterioration, especially in the form of oscillatory effects along the contours.
Furthermore, the wavelet bases used are built as one-dimensional wavelet tensor products. This induces a limitation of the capacity to represent certain structures while favoring certain directions. These defects, proper to the methods of image encoding by subbands, have led to preference being given to a representation of the image based on nested triangular meshes.
In the document [1], E. Quak suggests the simultaneous use of both techniques, associating a base of complementary wavelets with each mesh level in giving conditions on the ridges. He thus builds an explicit base of pre-wavelets on a triangular mesh. This technique is intended for the representation and compression of 3D digital models of terrains.
Quak's method of proceeding is described in greater detail in Appendix 1.
Appendix 2 for its part recalls the general principle and the broad lines of operation of the encoding method based on a hierarchy of nested meshes.
Although efficient, the known technique described in this Appendix 2 has certain limits.
In particular, one drawback of this method as proposed in [7], lies in the non-orthogonality of the functions φi(p) with the vector space Vp−1 generated by the functions φi(p−1). This implies a concentration of energy that is less efficient than it is in the case of the transforms using orthogonal transformation bases.
Furthermore, this raises a problem of cohabitation of different levels of resolution. Thus, when a vertex is at the boundary between a refined zone and an unrefined zone, it is not possible to choose an optimum value for this vertex for both resolutions. Indeed, for a vertex of this kind, choosing one of the values of one of the optimization levels will not give the optimum reconstruction except in the region corresponding to this level of refinement.
Furthermore, this sub-optimality of the representation is also a drawback in the context of a scalable encoding scheme. Indeed, it cannot be used to provide optimum reconstruction quality for intermediate bit rates.
It is a goal of the invention in particular to overcome these drawbacks of the prior art.
More specifically, it is a goal of the invention to provide a scalable image encoding technique and a corresponding decoding technique by which it is possible to obtain a quality of optimum reconstruction at each reconstruction level.
It is another goal of the invention to provide encoding and decoding techniques of this kind that necessitate a limited bit rate, for each reconstruction level.
It is also a goal of the invention to provide such encoding and decoding techniques, that enable the efficient processing of several images having the same structure (the same size and the same reference mesh).
It is yet another goal of the invention to provide a data and signal structure that makes it possible to optimize the bit rates necessary for the transmission and storage of images encoded in this way.
These goals, as well as others that shall appear more clearly here below, are achieved by means of a method for the encoding of at least one source image implementing a hierarchical mesh defining at least two nested spaces, each corresponding to a level n of decomposition of said mesh.